A company’s net cash flow in year nnn, denoted by PnP_nPn (in millions of dollars), follows a geometric progression with common ratio rrr.
You are given that:
Show that r r\,r satisfies the equation r2−2r−2=0r^2 - 2r - 2 = 0r2−2r−2=0.
Given that the sum of the cash flows over an infinite time period, ∑n=1∞Pn\sum_{n=1}^{\infty} P_n∑n=1∞Pn, is convergent,
find the exact value of P1P_1P1.
Hence, calculate the exact value of S∞S_\inftyS∞.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.